However, they remain four points shy of safety and Allardyce knows that the pressure will be incessant until they can force their way out of the relegation zone.

He said: “Yes, it’s massive, the pressure is constantly on you at this level and in this position, and you have to accept it because it’s our fault.

“We are only under that pressure because of our frailties and what we must do is continue to try to improve all the time by doing what I have said – you have to try to go out in every game and make fewer mistakes than the opposition, and then hopefully you keep a very important clean sheet and at the other end, your goalscorers punish the opposition.

“Whether you are playing better than the opposition or not doesn’t really matter. When you get the chance if you score it, it turns the game in your favour whether you deserved it or whether you didn’t.”

Sunderland certainly did not deserve the 30th-minute lead they took when Villa skipper Micah Richards inadvertently deflected Patrick van Aanholt’s shot into his own net with the visitors enjoying much the better of the first half.

But Allardyce’s men grew into the game and, after Carles Gil had drawn the visitors level with a stunning 63rd-minute volley, Defoe, who had enjoyed little service before the break, made the most of that which came his way after it to restore his side’s lead with 18 minutes remaining and then cement victory at the death.

Sunderland face a tough FA cup third round trip to Arsenal next week before heading for Swansea in another six-pointer, and Allardyce knows what his side does against the teams in the lower half of the table is likely ultimately to decide their fate.

He said: “It’s not rocket science to know that if you are going to get out of trouble, it’s the teams around you you have got to take the points from more than the bigger sides because the bigger sides, it’s so much more difficult to do that.

“If you get one of those or two of those in a season when you are in our position, then you are working a bit of a miracle. That’s your bonus points, then. As long as you have done it against the teams in and around you, then if you do it against the big boys it’s your bonus points.”

Asked if there had been any movement on any transfers, Allardyce said: “Movement? Slight movement in terms of there’s more progress made, but nothing to suggest we are going to sign anybody on the dotted line just yet.